Electrical machines usually comprise a housing-fixed stator as well as a rotor which can be moved relative thereto. The rotor may be supported so as to be rotatable with respect to the stator or so as to be linearly movable relative thereto, for instance. Electrical machines are ascribed to the electro-mechanical energy converters. In that context, they may operate as a motor or generator.
Electrical machines may be used for propelling motor vehicles, for instance. It is desirable here to achieve defined characteristics of the operational behavior of the electrical machine. The torque, the acoustic properties, the iron losses, the losses in permanent magnets in case such magnets are used, and the losses in windings are among these characteristics.
Electrical machines with concentrated windings are distinguished by compact designs compared to those with distributed windings. Winding types such as the fractional slot winding allow different combinations of the pole pair number and the number of the notches. The number of the pole pairs in the rotor is understood as the pole pair number, whereas the notches in the stator serve to receive the windings.
With electrical machines in motor vehicle drive systems, those with three electrical phases are most common among the multi-phase machines. Here, a three-phase machine can be connected to an electrical three-phase system with three phases which are shifted in their phase by 120° relative to each other.
Each magnetic pole pair in the rotor comprises two magnetic poles, a north pole and a south pole.
The number of the notches per pole and per phase is defined asq=Qs/(2*p*m),where m designates the number of the phases, Qs the number of the notches and p the number of the pole pairs.
Document US 2007/0194650 A1 describes an electrical machine comprising twelve notches and ten poles. In a machine of this type, the magnetomotive force (MMF) induced in operation by the stator is not distributed according to a simple sine wave. When analyzing the magnetomotive force and its harmonic components, for instance with a Fourier decomposition, it is rather obvious that numerous undesired harmonic components occur. Here, all harmonic components other than that used as the operating wave of the electrical machine are undesired as these may result in losses and, in addition, may cause undesired acoustic impairments.
It is therefore desirable to reduce the undesired harmonic components of the magnetomotive force or to eliminate them.
The operating wave may also be referred to as synchronized component. The torque of an electrical machine can be calculated from the electrical load distribution, or from the distribution of the magnetomotive force and the flux density distribution. A torque is generated whenever the harmonic order of the wave of the magnetomotive force and the harmonic order of a wave of the flux density coincide.
In order to produce a time-independent torque, the number of the pole pairs of the rotor in the considered minimum symmetry must coincide with the harmonic order of the main wave of the magnetomotive force, related to said symmetry. The required symmetry may be given, for instance, on the quarter perimeter or the half perimeter of a rotating electrical machine.
It is not necessarily the main wave which may be applied as the operating wave; using a higher-order harmonic component of the magnetomotive force is also possible.